摘要：
In credit risk modeling, Gaussian and Student’s t variates ariseprimarily from the copula method to retain certain correlation structures among defaultable assets. We propose efficient importance sampling algorithms to estimate lower tail probabilities of these two variates in any finite dimension. Variances of importance sampling estimators are shown asymptotically optimal by means of the large deviation theory and a truncation argument. Numerical comparisons with commercial codes, such as mvncdf.m and mvtcdf.m in Matlab, demonstrate robustness and efficiency of our proposed algorithms. Moreover, the flexibility of these algorithms can be seen from an application of probability estimation for the nth-to-default, i.e., the nth order statistic, given a credit portfolio.